The ellipsis indicates that something has been omitted. It could be something you’re trying to gloss over, like a mistake or an affair, or it could be something unutterably boring, like . . . I can’t think of anything boring enough. Note that the ellipsis can also be used to show that a conversation is trailing off, as above. A combination of a period and an ellipsis requires precise use of inner space.

The reason splitting infinitives is looked down upon is that in past centuries grammarians tried to lay Latin grammar the top of English and Latin infinitives are only one word, so there’s no possible way to split them. So for some reason somebody decided that English should not split infinitives either. An example of a split infinitive? A very famous one “To boldly go where no man has gone before”